Height of convective layer in planetary atmospheres with condensable and non-condensable greenhouse substances

Abstract. Convection reduces greenhouse effect by transporting a certain amount of non-radiative dynamic energy to the upper atmosphere, where this energy dissipates and radiates into space without interaction with greenhouse substances in the lower atmosphere. In this paper we show that the height of the convective layer z_c is finite and independent of atmospheric optical thickness τ_s at large values of the latter. We derive an analytical formula for z_c at large values of τ_s for condensable and non-condensable greenhouse substances. The formula obtained yields reasonable quantitative estimates of the observed height of convective layer on Venus and at low latitudes on Earth, where atmospheric thickness of water vapor is maximum.

The dissipative power of dynamic convective processes is limited by the incoming flux of solar radiation. Height of convective layer being finite, values of optical depth at the top of the convective layer and at the mean height of convective energy dissipation increase proportionally to the atmospheric optical thickness, while the contribution of convective energy fluxes to formation of the outgoing flux of thermal radiation proportionally diminishes. As far as optical thickness of condensable greenhouse substances grows exponentially with increasing surface temperature, the obtained results lead to the conclusion that the outgoing thermal radiation into space in the presence of convection tends exponentially to zero with increasing surface temperature, instead of reaching a finite plateau as suggested by earlier radiative-convective studies.